Bound state of the Hamiltonian of a system of two arbitrary particles on a lattice

The paper considers the Hamiltonian of a system of two arbitrary quantum particles on a lattice interacting by means of paired contact interactions of attraction. We prove the existence and uniqueness of the eigenvalues of the corresponding discrete Schrodinger operator as a function of the lattice dimension, the interaction energy of the particles, and the total quasi-pulse of the system. The set of bound states of the considered Hamiltonian is constructed.